(deftemplate binary-#
    (multislot name)
    (multislot digits))

(deftemplate add-binary-#s
    (multislot name-1)
    (multislot name-2))

(defrule add-binary-0 "Add the facts for the carry (temp) and the sum"
    (binary-# (name ?A) (digits $?))
    (binary-# (name ?B) (digits $?))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    =>
    (assert (temp 0))
    (assert (binary-# (name { ?A + ?B }) (digits )))
    )

(defrule add-binary-1 "The case that temp==0, first-A==1, and first-B==1"
    ?old-temp <- (temp 0)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&1))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&1))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-sum)
    (assert (temp 1))		;re-assert temp
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-2 "The case that temp==1, first-A==1, and first-B==1"
    (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&1))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&1))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 1 $?sum)))
    )

(defrule add-binary-3 "The case that temp==0, first-A==1, and first-B==0"
    (temp 0)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&1))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&0))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 1 $?sum)))
    )

(defrule add-binary-4 "The case that temp==1, first-A==1, and first-B==0"
    (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&1))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&0))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-5 "The case that temp==0, first-A==0, and first-B==1"
    (temp 0)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&0))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&1))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 1 $?sum)))
    )

(defrule add-binary-6 "The case that temp==1, first-A==0, and first-B==1"
    (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&0))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&1))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-7 "The case that temp==0, first-A==0, and first-B==0"
    (temp 0)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&0))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&0))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-B ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-8 "The case that temp==1, first-A==0, and first-B==0"
    ?old-temp <- (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&0))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&0))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-sum)
    (assert (temp 0))     ;re-assert temp
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-B
    (assert (binary-# (name { ?A + ?B }) (digits 1 $?sum)))
    )

(defrule add-binary-9 "The case that temp==0, no more digits in B, and any A"
    ?old-temp <- (temp 0)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A))
    ?old-B <- (binary-# (name ?B) (digits))
    ?old-add <- (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-add ?old-sum)
    (assert (binary-# (name { ?A + ?B }) (digits $?rest-A ?first-A $?sum)))
    )

(defrule add-binary-10 "The case that temp==1, no more digits in B, and first-A==0"
    ?old-temp <- (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&0))
    ?old-B <- (binary-# (name ?B) (digits))
    ?old-add <- (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-add ?old-sum)
    (assert (binary-# (name { ?A + ?B }) (digits $?rest-A 1 $?sum)))
    )

(defrule add-binary-11 "The case that temp==1, no more digits in B, and first-A==1"
    (temp 1)
    ?old-A <- (binary-# (name ?A) (digits $?rest-A ?first-A&1))
    (binary-# (name ?B) (digits))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-A ?old-sum)
    (assert (binary-# (name ?A) (digits $?rest-A)))    ;re-assert old-A
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-12 "The case that temp==0, no more digits in A, and any B"
    ?old-temp <- (temp 0)
    ?old-A <- (binary-# (name ?A) (digits))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B))
    ?old-add <- (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-add ?old-sum)
    (assert (binary-# (name { ?A + ?B }) (digits $?rest-B ?first-B $?sum)))
    )

(defrule add-binary-13 "The case that temp==1, no more digits in A, and first-B==0"
    ?old-temp <- (temp 1)
    ?old-A <- (binary-# (name ?A) (digits))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&0))
    ?old-add <- (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-add ?old-sum)
    (assert (binary-# (name { ?A + ?B }) (digits $?rest-B 1 $?sum)))
    )

(defrule add-binary-14 "The case that temp==1, no more digits in A, and first-B==1"
    (temp 1)
    (binary-# (name ?A) (digits))
    ?old-B <- (binary-# (name ?B) (digits $?rest-B ?first-B&1))
    (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-B ?old-sum)
    (assert (binary-# (name ?B) (digits $?rest-B)))    ;re-assert old-A
    (assert (binary-# (name { ?A + ?B }) (digits 0 $?sum)))
    )

(defrule add-binary-15 "The case that temp==1, no more digits in B, and no more digits in A"
    ?old-temp <- (temp 1)
    ?old-A <- (binary-# (name ?A) (digits))
    ?old-B <- (binary-# (name ?B) (digits))
    ?old-add <- (add-binary-#s (name-1 ?A) (name-2 ?B))
    ?old-sum <- (binary-# (name { ?A + ?B }) (digits $?sum))
    =>
    (retract ?old-temp ?old-A ?old-B ?old-add ?old-sum)
    (assert (binary-# (name { ?A + ?B }) (digits 1 $?sum)))
    )


;Facts assertion for testing
(assert (binary-# (name A) (digits 1 0 1 1 1)))
(assert (binary-# (name B) (digits   1 1 1 0)))
(assert (add-binary-#s (name-1 A) (name-2 B)))
(run)

(assert (binary-# (name C) (digits 1)))
(assert (binary-# (name D) (digits 1 1 1 0)))
(assert (add-binary-#s (name-1 C) (name-2 D)))
(run)

(assert (binary-# (name E) (digits 1 0 0 0)))
(assert (binary-# (name F) (digits 0 1 1 1 0)))
(assert (add-binary-#s (name-1 E) (name-2 F)))
(run)